Q 11-06-098JEE MainJEE Main 2024 (30 Jan, Shift 2)Medium
Two discs of moment of inertia $I_1 = 4\ \text{kg m}^2$ and $I_2 = 2\ \text{kg m}^2$ about their central axes and normal to their planes, rotating with angular speeds $10\ \text{rad s}^{-1}$ and $4\ \text{rad s}^{-1}$ respectively, are brought into contact face to face with their axes of rotation coincident. The loss in kinetic energy of the system in the process is ______ J.
Numerical value type. Enter your answer.
Answer: 24
Assuming both rotate in the same sense, angular momentum is conserved:
$$\omega = \frac{4\times10 + 2\times4}{6} = 8\ \text{rad s}^{-1}$$
$$K_i = \tfrac12(4)(100) + \tfrac12(2)(16) = 216\ \text{J},\qquad K_f = \tfrac12(6)(64) = 192\ \text{J}$$
Loss $= 24\ \text{J}$.
Solution by Sreeraj P, M.Sc Physics